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  • Triticum aestivum  (263)
  • CR: 5.17
  • seaweed
  • Springer  (541)
  • 1985-1989  (228)
  • 1980-1984  (313)
  • 1925-1929
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  • 1
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    Computing 25 (1980), S. 317-335 
    ISSN: 1436-5057
    Keywords: AMS (MOS): 65L65 ; CR: 5.17 ; AMS (MOS): 65L65 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract In this paper a general procedure to obtain spline approximations for the solutions of initial value problems for ordinary differential equations is presented. Several well-known spline approximation methods are included as special cases. It is common practice to partition the interval for which the initial value problem is defined into equidistant subintervals and to construct successively the spline approximation; thereby the spline function has to satisfy certain conditions at the knots. In the general procedure presented here additional knots are admitted in every subinterval. At these points which need not be equally spaced the spline approximation has to fulfill analogous conditions as at the original knots. Convergence and divergence theorems are proved; especially the influence of the additional knots on convergence and divergence of the method is investigated.
    Notes: Zusammenfassung In dieser Arbeit wird ein allgemeines Verfahren zur Erzeugung von Splineapproximationen für die Lösungen von Anfangswertproblemen bei gewöhnlichen Differentialgleichungen vorgestellt. Einige der bekannten Spline-approximationsmethoden sind als Spezialfälle enthalten. Eine gängige Vorgehensweise besteht darin, das Intervall, über dem das Anfangswertproblem gegeben ist, in äquidistante Teilintervalle zu zerlegen und dann sukzessive die Splineapproximation zu definieren. Hierbei wird gefordert, daß die Spline-approximation in den Knoten gewisse Bedingungen erfüllt. Bei dem hier betrachteten allgemeinen Verfahren werden in den einzelnen Teilintervallen noch zusätzliche Zwischenknoten eingeführt. In diesen Punkten, die nicht äquidistant sein müssen, werden für die Splineapproximation analoge Bedingungen wie in den Hauptknoten vorgeschrieben. Konvergenz- und Divergenzsätze werden bewiesen, insbesondere wird der Einfluß der Zwischenknoten auf Konvergenz und Divergenz des Verfahrens untersucht.
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  • 2
    ISSN: 1436-5057
    Keywords: 65L05 ; CR: 5.17 ; Numer. Analysis ; verallgemeinerte Runge-Kutta-Methoden ; steife Probleme
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract Adaptive Runge-Kutta-methods are considered. Investigations of stability for these linear implicit methods are studied. For the application a LS-stable method of order four with an adaptive stepsize control is proposed. Test results for 25 stiff initial value problems for different tolerances are discussed.
    Notes: Zusammenfassung Es werden adaptive Runge-Kutta-Verfahren betrachtet und Stabilitätsuntersuchungen für diese linear impliziten Methoden durchgeführt. Für die Anwendung wird ein LS-stabiles Verfahren vierter Ordnung mit einer angepaßten Schrittweitenkontrolle vorgeschlagen. Testergebnisse von 25 stiff Anfangswertproblemen für verschiedenen Toleranzen werden diskutiert.
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  • 3
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    Numerische Mathematik 40 (1982), S. 179-199 
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; Primary 65N30 ; Secondary 35R35 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Two problems are considered in the paper: the first of them is connected with elliptic variational inequalities and consists in developing a moving obstacle algorithm for approximating the unknown free boundary; the other problem is linked with numerical solution of the Stefan problem, which is formulated in the similar way as in the elliptic case. Some computational aspects are also discussed in the paper.
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  • 4
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    Numerische Mathematik 40 (1982), S. 207-227 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65M30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Several regularization methods for parabolic equations backwards in time together with the usual additional constraints for their solution are considered. The error of the regularization is estimated from above and below. For a “boundary value problem in time”-method, finite elements as well as a time discretization are introduced and the error with respect to the regularized solution is estimated, thus giving an overall error of the discrete regularized problem. The algorithm is tested in simple numerical examples.
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  • 5
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    Numerische Mathematik 43 (1984), S. 105-119 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A new formulation of the Dirichlet problem for the biharmonic operator is presented. This gives rise to a simple numerical method to solve the above problem. Convergence is proved in the unidimensional case. Numerical results in one and two dimensional test problems are presented.
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  • 6
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    Numerische Mathematik 43 (1984), S. 175-198 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 L 10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present a difference scheme for solving a semilinear singular perturbation problem with any number of turning points of arbitrary orders. It is shown that a solution of the scheme converges, uniformly in a perturbation parameter, to that of the continuous problem.
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  • 7
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65 N 30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Summary This paper uses Augmented Lagrangian techniques for the numerical solution of equilibrium problems of compressible hyperelastic bodies subjected to large deformations. The resulting method is illustrated by several numerical examples.
    Notes: Résumé Cet article applique les techniques de Lagrangien Augmenté à la résolution numérique des problèmes d'équilibre de corps hyperélastiques compressibles soumis à de grandes déformations. La méthode obtenue est illustrée par plusieurs exemples numériques.
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  • 8
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    Numerische Mathematik 39 (1982), S. 221-230 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper Adams type methods for the special case of neutral functional differential equations are examined. It is shown thatk-step methods maintain orderk+1 for sufficiently small step size in a sufficiently smooth situation. However, when these methods are applied to an equation with a “non-smooth” solution the order of convergence is only one. Some computational considerations are given and numerical experiments are presented.
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  • 9
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    Numerische Mathematik 39 (1982), S. 309-324 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65L10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A method for improvement of the numerical solution of differential equations by incorporation of asymptotic approximations is investigated for a class of singular perturbation problems. Uniform error estimates are derived for this method when implemented in known difference schemes and applied to linear second order O.D.E.'s. An improvement by a factor ofε n+1 can be obtained (where ɛ is the “small” parameter andn is the order of the asymptotic approximation) for a small amount of extra work. Numerical experiments are presented.
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  • 10
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    Numerische Mathematik 39 (1982), S. 341-350 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We discuss the construction of three-point finite difference approximations and their convergence for the class of singular two-point boundary value problems: (x α y′)′=f(x,y), y(0)=A, y(1)=B, 0〈α〈1. We first establish a certain identity, based on general (non-uniform) mesh, from which various methods can be derived. To obtain a method having order two for all α∈(0,1), we investigate three possibilities. By employing an appropriate non-uniform mesh over [0,1], we obtain a methodM 1 based on just one evaluation off. For uniform mesh we obtain two methodsM 2 andM 3 each based on three evaluations off. For α=0,M 1 andM 2 both reduce to the classical second-order method based on one evaluation off. These three methods are investigated, theirO(h 2)-convergence established and illustrated by numerical examples.
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  • 11
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    Numerische Mathematik 39 (1982), S. 371-404 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65 N 30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The purpose of this paper is to study the approximation of the Von Karman equations by the mixed finite element scheme of Miyoshi and to follow the solutions arcs at a neighbourhood of the first eigenvalue of the linearized problem. This last problem is solved by a continuation method.
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  • 12
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    Numerische Mathematik 39 (1982), S. 449-463 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65L65 ; CR: 5.17 ; AMS (MOS): 65L65 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Summary In [10] a general procedureV is presented to obtain spline approximations by collocation for the solutions of initial value problems for first order ordinary differential equations. In this paper the attainable order of convergence with respect to the maximum norm is characterized in dependence of the parameters involved inV; in particular the appropriate choice of the collocation points is considered.
    Notes: Zusammenfassung In [10] ist ein allgemeines VerfahrenV beschrieben, das die Lösungen von Anfangswertproblemen bei gewöhnlichen Differentialgleichungen erster Ordnung durch Splines approximiert. Die Konstruktion der Splines erfolgt hierbei mittels Kollokation. In dieser Arbeit wird die maximal erreichbare Konvergenzordnung vonV bezüglich der Maximumnorm in Abhängigkeit aller Parameter vonV charakterisiert, insbesondere wird auf die geeignete Wahl der Kollokationsknoten eingegangen.
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  • 13
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    Numerische Mathematik 40 (1982), S. 169-177 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The stability and accuracy of some explicit nonlinear methods for the numerical integration of stiff systems of ordinary differential equations are investigated. It is shown, that in the general case they can produce the essential error. The special class of stiff systems is singled out, for which these methods are highly efficient. Some numerical results are also presented.
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  • 14
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    Numerische Mathematik 40 (1982), S. 319-328 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65J05, 65L15 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Although multiparameter eigenvalue problems, as for example Mathieu's differential equation, have been known for a long time, so far no work has been done on the numerical treatment of these problems. So in this paper we extend the spectral theory for one parameter (cf. [7, II, VII]) to multiparameter eigenvalue problmes, formulate in the framework of discrete approximation a convergent numerical treatment, establish algebraic bifurcation equations for the intersection points of the eigenvalue curves and illustrate this with some numerical examples.
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  • 15
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    Numerische Mathematik 40 (1982), S. 373-406 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30, 65M20 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We extend in this paper the analysis of a posteriori estimates of the space discretization error presented in a previous paper [3] for time-independent space meshes. In the context of the model problem studied there, results are given relating the effectiveness of the error estimator to properties of the solution, space meshes, and manner in which the meshes change. A procedure based upon this theory is presented for the adaptive construction of time-dependent meshes. The results of some computational experiments show that this procedure is practically very effective and suggest that it can be used to control the space discretization error in more general problems.
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  • 16
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    Numerische Mathematik 41 (1983), S. 373-398 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The paper introduces a new semi-implicit extrapolation method especially designed for the numerical solution of stiff systems of ordinary differential equations. The existence of a quadratic asymptotic expansion in terms of the stepsize is shown. Moreover, the new discretization is analyzed in the light of well-known stability models. The efficiency of the new integrator is clearly demonstrated by solving a series of challenging test problems including real life examples.
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  • 17
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    Numerische Mathematik 41 (1983), S. 345-371 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Maximum-norm stability and error estimates of best approximation and nonsmooth data types are derived for the approximate solution of a parabolic equation in one space variable, using the continuous in time Galerkin method based on piecewise polynomial approximating functions on a quasi-uniform mesh.
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  • 18
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We study the difference equations obtained when a linear multistep method is applied to the scalar test equationdy/dt=λy and constant stepsizeh. LetS be the region of the absolute stability of the method, and letD be a closed subset ofS (on the Riemann sphere $$\mathbb{C}$$ ). It is shown that the solutions of these difference equations are bounded forn≧0, uniformly for λh∈D.S is itself closed in $$\mathbb{C}$$ iff ∂S is free of cusps. The question is studed by means of contractivity analysis and a matrix theorem, derived from the matrix theorem of Kreiss.
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  • 19
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    Numerische Mathematik 41 (1983), S. 399-422 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary The paper presents a new theory for joint order and stepsize control in extrapolation methods. This theory defines a locally optimal order that can be determined along any trajectory to be computed. In addition, Shannon's information theory is applied to derive some ideal convergence model that is expected to describe the behavior of an extrapolation method over a large set of test problems. Extensive numerical comparisons document a drastic acceleration in stiff integration and a mild acceleration in non-stiff integration by the new device. Moreover, a significant increase in reliability, robustness, and portability of the extrapolation codes is achieved.
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  • 20
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    Numerische Mathematik 42 (1983), S. 299-310 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A new approach to the problem of numerically integrating stiff differential systems is described. In this approach a linear multistep method (the basic method) is split into a kind of predictor-corrector scheme, where the predictor is also implicit. If this splitting is done in an appropriate manner, the modified method has considerably better stability properties than the basic method. As a result, splitting methods are particularly useful for problems where conventional integration methods experience stability difficulties. In particular some highly stable split linear multistep methods based on backward differentiation formulae are derived and a highly stable variable step implementation is proposed.
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  • 21
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    Numerische Mathematik 42 (1983), S. 311-322 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 N 30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper presents Galerkin approximations for solutions of two dimensional interface problems by solving corresponding boundary integral equations. These are obtained by simple layer potential operators only. Due to the strong ellipticity of the integral equations the Galerkin procedure converges with optimal order. Smoothness of the given data implies high convergence rates for the layers.
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  • 22
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    Numerische Mathematik 42 (1983), S. 349-357 
    ISSN: 0945-3245
    Keywords: AMS(MOS) 65L05 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper theD-stability properties of some classes of perturbed collocation methods are investigated. Among others we show the implicit Runge-Kutta methods described by Ehle-Chipman to beD-stable. We also give implicit Runge-Kutta methods that are bothD-stable andA-stable but notB-stable. Finally we indicate in what senseB-stability is stronger thanA-stability together withD-stability. The results of this paper are based on recent results of Nørsett and Wanner on perturbed collocation methods.
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  • 23
    ISSN: 1432-0789
    Keywords: Wheat ; Paddy straw compost ; N and P enrichment ; Rock phosphate ; Pyrite ; Triticum aestivum ; Nutrient uptake
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Geosciences , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary A nutrient-rich compost from paddy straw was prepared using urea and Mussoorie rock phosphate for N and P enrichment respectively. Inorganic N was partly conserved in the compost by the addition of pyrite. Citric-acid-soluble P also increased with the addition of pyrite. Compost containing about 1.6% total N and 3.3% total P was found to be a good source of P for a wheat crop and also supplied a significant amount of N to the plants.
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  • 24
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    Biology and fertility of soils 3 (1987), S. 199-204 
    ISSN: 1432-0789
    Keywords: Phosphatases ; Rhizosphere ; Organic phosphorus ; Allium cepa ; Brassica oleracea ; Triticum aestivum ; Trifolium alexandrinum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Geosciences , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary The distribution of phosphatase activity and of phosphate fractions of the soil in the proximity of roots was studied in order to evaluate the significance of phosphatases in P nutrition of various plants (Brassica oleracea, Allium cepa, Triticum aestivum, Trifolium alexandrinum). A considerable increase in both acid and alkaline phosphatase activity in all the four soil-root interfaces was observed. Maximum distances from the root surface at which activity increases were observed ranged from 2.0 mm to 3.1 mm for acid phosphatase and from 1.2 mm to 1.6 mm for alkaline phosphatase. The increase in phosphatase activity depended upon plant age, plant species and soil type. A significant correlation was noticed between the depletion of organic P and phosphatase activity in the rhizosphere soil of wheat (r = 0.99**) and clover (r = 0.97**). The maximum organic P depletion was 65% in clover and 86% in wheat, which was observed within a distance from the root of 0.8 mm in clover and 1.5 mm in wheat. Both the phosphatases in combination appear to be responsible for the depletion of organic P.
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  • 25
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    Biology and fertility of soils 5 (1987), S. 76-82 
    ISSN: 1432-0789
    Keywords: Biomass accumulation ; Decomposition ; Litter ; Soil organic matter ; Soil respiration ; 14C deposition ; Triticum aestivum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Geosciences , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary In a field experiment with 14C-labeled winter wheat conducted in the north-central region of the United States, crop-accumulated carbon (grain excluded) returned to the soil was found to be 542 g m−2 year−1. Almost half of the carbon from the underground compartment was released in the form of CO2 during the first 3 months after harvest due to very favorable conditions for biological activity. After 18 months, no less than 80% of the carbon from the plant residues was mineralized. About 16% of straw carbon and 24% of root carbon was transferred into soil organic matter. The annual rate of soil organic matter decomposition was approximated as 1.7%.
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  • 26
    ISSN: 1432-0789
    Keywords: Triticum aestivum ; T. turgidum ; Nitrogen fixation ; Field inoculation ; Acetylene reduction assay (ARA)
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Geosciences , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Eight commercial Israeli spring wheat cultivars (six Triticum aestivum and two T. turgidum) grown with 40 and 120 kg N/ha were tested for responses to inoculation with Azospirillum brasilense. At the low level of N fertilization (40 kg/ha), five cultivars showed significant increases in plant dry weight measured at the milky ripe stage; however, by maturation only the cultivar “Miriam” showed a significant increase in grain yield. Two cultivars, which had shown a positive inoculation effect at the earlier stages, had a significant decrease in grain yield. No significant effect of inoculation was found at the high N level. To confirm those results, four wheat (T. aestivum) cultivars were tested separately over 4 years in 4 different locations under varying N levels. Only Miriam showed a consistently positive effect of Azospirillum inoculation on grain yield. Inoculation increased the number of roots per plant on Miriam compared with uninoculated plants. This effect was found at all N levels. Nutrient (N, P and K) accumulation and number of fertile tillers per unit area were also enhanced by Azospirillum, but these parameters were greatly affected by the level of applied N. It is suggested that the positive response of the spring wheat cultivar “Miriam” to Azospirillum inoculation is due to its capacity to escape water stresses at the end of the growth season.
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  • 27
    ISSN: 1432-0789
    Keywords: Azospirillum brasilense ; Triticum aestivum ; Inoculation ; N and dry matter yield ; N percentages in plant parts ; Associative N2 fixation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Geosciences , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Wheat plants (Triticum aestivum) grown in pots and in the field under the Mediterranean climate of the south of France were inoculated with a strain of Azospirillum brasilense. Comparisons with non-inoculated plants grown under the same conditions showed significant responses to inoculation with an increase in the number of fertile tillers, shoot and root dry weight, and root to shoot biomass ratio. The roots of inoculated plants attracted relatively more assimilates than those of the control plants until a late stage of growth (heading stage) but the rhizosphere respiration expressed per unit of root growth was not increased by inoculation. Nitrogen yield, both total and in grains, was also enhanced; however, N percentages of all aerial parts of the plants grown in pots were always statistically lower after inoculation than in the control. At maturity, the N % in seeds was 1.81 and 2.45, respectively. The possible mechanisms of this effect of inoculation under the experimental conditions of this study are discussed.
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  • 28
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    Biology and fertility of soils 7 (1988), S. 67-70 
    ISSN: 1432-0789
    Keywords: Root activity ; Soil C mineralization ; 14C-labelled plant material ; Decomposition stages ; Wheat ; Triticum aestivum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Geosciences , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Two different soils were amended with 14C-labelled plant material and incubated under controlled laboratory conditions for 2 years. Half the samples were cropped with wheat (Triticum aestivum) 10 times in succession. At flowering, the wheat was harvested and the roots removed from the soil, and a new crop was started. Thus, the soil was continuously occupied by predominantly active root systems. The remaining samples were maintained without plants under the same conditions. The aim of the experiment was to study the effects of active roots on C-mineralization rates during different stages of decomposition and during long-term incubation. During the first 200 days, corresponding to the active decomposition stages, the roots weakly reduced 14C mineralization. With a lower level of decomposition, when more than 60% of the initial 14C was mineralized and when the available nutrients were markedly exhausted by plant uptake, the roots stimulated 14C mineralization.[/ p]
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  • 29
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    Biology and fertility of soils 7 (1988), S. 71-78 
    ISSN: 1432-0789
    Keywords: Root activity ; Rhizosphere ; C metabolism ; Microbial biomass ; Microbial activity ; Wheat ; Triticum aestivum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Geosciences , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Two different soils were amended with 14C-labelled plant material and incubated under controlled laboratory conditions for 2 years. Half the samples were cropped with wheat (Triticum aestivum) 10 times in succession. At flowering, the wheat was harvested and the old roots removed from the soil, so that the soil was continuously occupied by predominantly active root systems. The remaining samples were maintained without plants under the same conditions. During the initial stages of high microbial activity, due to decomposition of the labile compounds, the size of the total microbial biomass was comparable for both treatments, and the metabolic quotient (qCO2-C = mg CO2-C·mg−1 Biomass C·h−1) was increased by the plants. During the subsequent low-activity decomposition stages, after the labile compounds had been progressively mineralized, the biomass was multiplied by a factor of 2–4 in the presence of plants compared to the bare soils. Nevertheless, qCO2-C tended to reach similar low values with both treatments. The 14C-labelled biomass was reduced by the presence of roots and qCO2-14C was increased. The significance of these results obtained from a model experiment is discussed in terms of (1) the variation in the substrate originating from the roots and controlled by the plant physiology, (2) nutrient availability for plants and microorganisms, (3) soil biotic capacities and (4) increased microbial turnover rates induced by the roots.
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  • 30
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    Biology and fertility of soils 4 (1987), S. 37-40 
    ISSN: 1432-0789
    Keywords: Azospirillum brasilense ; Azospirillum amazonense ; rate reductase ; Inoculation ; Wheat ; Triticum aestivum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Geosciences , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Three field experiments with wheat were conducted in 1983, 1984, and 1985 in Terra Roxa soil in Paraná, the major Brazilian wheat-growing region, to study inoculation effects of various strains of Azospirillum brasilense and A. amazonense. In all three experiments inoculation with A. brasilense Sp 245 isolated from surface-sterilized wheat roots in Paraná produced the highest plant dry weights and highest N% in plant tops and grain. Grain yield increases with this strain were up to 31 % but were not significant. The application of 60 or 100 kg N ha−1 to the controls increased N accumulation and produced yields less than inoculation with this strain. Another A. brasilense strain from surface-sterilized wheat roots (Sp 107st) also produced increased N assimilation at the lower N fertilizer level but reduced dry weights at the high N level, while strain Sp 7 + Cd reduced dry weights and N% in the straw at both N levels. The A. amazonense strain isolated from washed roots and a nitrate reductase negative mutant of strain Sp 245 were ineffective. Strains Sp 245 and Sp 107st showed the best establishment within roots while strain Cd established only in the soil.
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    Biology and fertility of soils 4 (1987), S. 41-46 
    ISSN: 1432-0789
    Keywords: Competition ; Migration ; Colonization potential ; Replica printing ; Triticum aestivum ; Pseudomonas fluorescens ; Bacillus subtilis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Geosciences , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Colonization patterns of Pseudomonas fluorescens and Bacillus subtilis on roots of wheat seedlings growing on water agar were studied qualitatively by replica printing and quantitatively by the plate count method. The results indicated a stronger colonization potential for P. fluorescens (up to 107 cfu/cm root) than for B. subtilis (up to 105 cfu/cm root). Although the numbers of both species were lower when inoculated together, the observed colonization patterns on the roots were comparable to those found with single inoculations. For none of these bacteria was active migration along the root surface in any direction observed, indicating that distal positions are reached mainly by a passive displacement on the root tip and elongating cells. Ecological implications of the observed phenomena are discussed.
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    Biology and fertility of soils 5 (1987), S. 31-35 
    ISSN: 1432-0789
    Keywords: Gaeumannomyces graminis ; VegVetative growth ; Pathogenicity ; Herbicides ; Diquat+paraquat ; Glyphosate ; Dicamba ; Trifluralin ; Chlorsulfuron ; Chlorthal dimethyl ; Triticum aestivum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Geosciences , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary The effects of Spray Seed (diquat + paraquat), Roundup (glyphosate), Banvel-D (dicamba), Treflan (trifluralin), Glean (chlorsulfuron) and Dacthal (chlorthal dimethyl) at concentrations of 0–500 ppm product on the vegetative growth, vigour and pathogenicity of Gaeumannomyces graminis var. tritici (Ggt) on wheat were examined. All herbicides with the exception of dicamba and chlorsulfuron inhibited fungal growth on potato dextrose agar (PDA) at concentrations 10–500-fold of rates recommended for use in the field. The vegetative growth of the pathogen growing out of straw colonized on PDA supplemented with 100 ppm diquat + paraquat or glyphosate was reduced by 47.4% and 42.4%, respectively. When portions of these colonies were subcultured onto unamended PDA, their growth and the pathogenicity of straw pieces colonized by these subcultures were found to be unaltered. Straw colonized by Ggt on agar amended with concentrations of diquat + paraquat or at all concentrations of glyphosate produced less root disease in wheat seedlings in comparison to those colonized on unamended agar. It is proposed that the reduced pathogenicity of inocula prepared on agar amended with these two herbicides is due to poor colonization by the pathogen of straw on these media, and that a similar effect on saprophytic colonization in the field could lead to a reduction in the field inocula of the pathogen.
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  • 33
    ISSN: 1432-0789
    Keywords: Biopores ; Root growth ; Transpiration ; Simulations ; Mechanical impedance ; Triticum aestivum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Geosciences , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary The use of vertical biopores by wheat (Triticum aestivum) seminal roots for easy access to the subsoil and the consequences for plant water supply and yield has been investigated by computer simulation. Parameters included were: biopore density and diameter, depth of cultivation and strength of the subsoil — all under a wide range of seasonal weather conditions. The model predicts that biopores add significantly to root penetration at depth, even at a density of 0.1% v/v of small, vertical pores, while 1.5% to 2.0% v/v can ensure maximum root penetration. When the growing season is shorter a larger number of biopores is needed to ensure timely root penetration to depth. With shallow tillage, biopores occur closer to the soil surface, and their importance is increased. Deeper root penetration invariably gives greater water uptake and transpiration, but may have a negative effect on grain yield, especially under the driest climatic conditions. An increase in early water use may result in less soil water being available during the grain-filling period. The effect of biopores on plant transpiration varies from year to year, depending on the amount of rain and its distribution in time, and on the amount of soil water stored at time of sowing.
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  • 34
    ISSN: 1432-0983
    Keywords: Triticum aestivum ; Plant mitochondrial DNA ; Ribosomal genes ; Sequence rearrangements
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    Topics: Biology
    Notes: Summary The nucleotide sequence of the wheat mitochondrial 26S ribosomal RNA gene and flanking regions was determined and compared with mitochondrial 26S rRNA genes from maize and Oenothera. All three genes exhibit a high degree of homology except within two variable regions. When the plant mitochondrial 26S rRNA genes are compared with Escherichia coli 23S rRNA and chloroplast 23S and 4.5S rRNA genes, a third variable region is apparent close to the 3′ end of the gene. The 5′ and 3′ ends of the wheat mitochondrial gene were determined by S1 nuclease mapping. Computer analysis of the wheat mitochondrial gene revealed several small sequences present either in the 5′ region of the 26S rRNA gene or in the 18S rRNA gene.
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  • 35
    ISSN: 1432-0983
    Keywords: Triticum aestivum ; Genomic variability ; Mitochondrial DNA ; Somatic tissue culture ; Regeneration ability
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    Topics: Biology
    Notes: Summary Embryogenic and non-embryogenic long-term callus cultures of hexaploid wheat exhibit differences in the organization of their mitochondrial genome. Embryogenic and non-embryogenic fractions of callus cultures initiated from immature embryos of the wheat cultivar “Chinese Spring” have been isolated and subsequently subcultured. DNA-DNA hybridization experiments using labelled cloned wheat mitochondrial DNA fragments have shown that the mitochondrial DNA organization of embryogenic subcultures derived from embryogenic parts of “Chinese Spring” calli is closely related to that of the initial “Chinese Spring” calli, while non-embryogenic subcultures derived from non-embryogenic fragments of “Chinese Spring” calli exhibit a mitochondrial DNA organization similar to that found in non-embryogenic calli derived from cultivar “Aquila”. In addition, somatic tissue cultures initiated from three other non-embryogenic wheat cultivars (“Talent”, “Thésée” and “Capitole”) display mitochondrial DNA arrangements similar to those found in cultivar “Aquila”. These results strongly suggest that, in wheat callus cultures, a particular mitochondrial genome organization is correlated with the ability of cultured cells to regenerate whole plants.
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    Nutrient cycling in agroecosystems 20 (1989), S. 59-66 
    ISSN: 1573-0867
    Keywords: Ammonia volatilization ; nitrogen leaching ; denitrification ; time of N application ; wheat ; Triticum aestivum ; Triticale ; irrigation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract Grain yield, nitrogen (N) assimilation, ammonia (NH3) volatilization, denitrification and fertilizer N distribution were examined in three commercially grown cereal crops; two were sown into conventionally tilled fields, while the third was direct drilled into an untilled field. The crops were top dressed with urea at establishment, tillering or ear initiation. Crop yield and N assimilation were measured in 16 m by 2.5 m plots receiving 0, 35, 70, 105, 140 or 175 kg N ha−1. A mass balance micrometeorological technique was used to measure NH3 volatilization, and other fertilizer N transformations and transfers were studied using15N labelled urea in microplots. On the conventionally tilled sites application of urea increased the grain yield of wheat from 3.9 to 5.5 t ha−1, when averaged over the five application rates, three application times and two sites. There were no site or application time effects. However, on the direct drilled site, time of application had a significant effect on grain yield. When urea was applied at establishment, grain yield was not significantly increased and the mean yield (2.81 t ha−1) was less than that obtained from treatments fertilized at tillering or ear initiation (4.09 and 4.0 t ha−1, respectively). Much of the variation in grain yield at the no-till site could be ascribed to differences in NH3 volatilization. At the no-till site, NH3 losses were equivalent to 24, 12 and 1% of the N applied at establishment, tillering and ear initiation, respectively. Negligible volatilization of NH3 occurred at the other sites. The surface soil at the no-till site had the highest urease activity and the soil was covered with alkaline ash resulting from stubble burning. Plant recovery of fertilizer N did not vary with application time on conventionally tilled sites (mean 62%). However, plant recovery of15N applied to the no-till site at establishment (35% of the applied N) was significantly less than that from plots where the application was delayed (45% at tillering and 55% at ear initiation, respectively). Leaching of N to below 300 mm depth was minimal (0 to 5% of the applied N). The calculated denitrification losses ranged from 1% to 14% of the applied N. The results show that the relative importance of NH3 volatilization, leaching and denitrification varied with site and fertilization time. The importance of the various N loss mechanisms needs to be taken into account when N fertilization strategies are being developed.
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    Numerische Mathematik 34 (1980), S. 235-246 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary A class of extended backward differentiation formulae suitable for the approximate numerical integration of stiff systems of first order ordinary differential equations is derived. An algorithm is described whereby the required solution is predicted using a conventional backward differentiation scheme and then corrected using an extended backward differentiation scheme of higher order. This approach allows us to developL-stable schemes of order up to 4 andL(α)-stable schemes of order up to 9. An algorithm based on the integration formulae derived in this paper is illustrated by some numerical examples and it is shown that it is often superior to certain existing algorithms.
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    Numerische Mathematik 35 (1980), S. 127-142 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 34G05, 65L05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary A class of approximation schemes of arbitrary accuracy, generated by a two-step recurrence relation, is devised for evolution equations of the second order. The schemes are effected via a specially constructed family of rational approximations to cos τ for τ≧0 and yield computationally efficient methods for systems of second-order ordinary differential equations and semidiscrete approximations for initial-boundary value problems for second-order hyperbolic equations.
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    Numerische Mathematik 35 (1980), S. 143-162 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65M15, 65N30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary We study the error due to the discretization in time of a nonlinear parabolic problem by a multistep method. Error estimates are obtained if the method is of the orderp (p〉1) and stronglyA(Θ)-stable $$\left( {0〈 \Theta〈 \frac{\pi }{2}} \right)$$ . The method is also applied to the Navier-Stokes equations in two dimensions.
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    Numerische Mathematik 35 (1980), S. 231-240 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L10 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary The homotopy method is a frequently used technique in overcoming the local convergence nature of multiple shooting. In this paper sufficient conditions are given that guarantee the homotopy process to be feasible. The results are applicable to a class of two-point boundary value problems. Finally, the numerical solution of two practical problems arising in physiology is described.
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    Numerische Mathematik 35 (1980), S. 257-276 
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65M10 ; CR: 5.17
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    Topics: Mathematics
    Description / Table of Contents: Résumé Considérons une équation d'évolution parabolique linéaire associée à un opérateur linéaireA(t) dépendant du tempst. Nous développons dans cet article une méthode de discrétisation, basée sur les méthodes linéaires à pas multiples, traitant de manière implicite une partie de l'opérateurA(t) indépendante du temps, l'autre partie est traitée de manière explicite. Nous étudions la stabilité et la convergence de cette méthode.
    Notes: Summary Let us consider a linear parabolic equation which is associated with a time dependent operatorA(t). In this paper, we present a method, which is founded on linear multistep methods, which discretize a time-independent part of the operatorA(t) in an implicit way, and the other part in an explicit way. We study stability and convergence for this method.
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    Numerische Mathematik 35 (1980), S. 315-341 
    ISSN: 0945-3245
    Keywords: AMS(MOS) ; 65N30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary We present here some new families of non conforming finite elements in ℝ3. These two families of finite elements, built on tetrahedrons or on cubes are respectively conforming in the spacesH(curl) andH(div). We give some applications of these elements for the approximation of Maxwell's equations and equations of elasticity.
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    Numerische Mathematik 35 (1980), S. 381-404 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary We study in this paper the convergence of a new mixed finite element approximation of the Navier-Stokes equations. This approximation uses low order Lagrange elements, leads to optimal order of convergence for the velocity and the pressure, and induces an efficient numerical algorithm for the solution of this problem.
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    Numerische Mathematik 45 (1984), S. 105-116 
    ISSN: 0945-3245
    Keywords: AMS(MOS) 65 N 30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary We study a superconvergence phenomenon which can be obtained when solving a 2nd order elliptic problem by the usual linear elements. The averaged gradient is a piecewise linear continuous vector field, the value of which at any nodal point is an average of gradients of linear elements on triangles incident with this nodal point. The convergence rate of the averaged gradient to an exact gradient in theL 2-norm can locally be higher even by one than that of the original piecewise constant discrete gradient.
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    Numerische Mathematik 45 (1984), S. 201-206 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Bulirsch and Stoer have shown how to construct asymptotic upper and lower bounds on the true (global) errors resulting from the solution by extrapolation of the initial value problem for a system of ordinary differential equations. It is shown here how to do this for any one-step method endowed with an asymptotically correct local error estimator. The one-step method can be changed at every step.
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    Numerische Mathematik 37 (1981), S. 257-277 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
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    Notes: Summary In theh-version of the finite element method, convergence is achieved by refining the mesh while keeping the degree of the elements fixed. On the other hand, thep-version keeps the mesh fixed and increases the degree of the elements. In this paper, we prove estimates showing the simultaneous dependence of the order of approximation on both the element degrees and the mesh. In addition, it is shown that a proper design of the mesh and distribution of element degrees lead to a better than polynomial rate of convergence with respect to the number of degrees of freedom, even in the presence of corner singularities. Numerical results comparing theh-version,p-version, and combinedh-p-version for a one dimensional problem are presented.
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    Numerische Mathematik 37 (1981), S. 405-421 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65 N 30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Abstract The discretization by finite elements of a model variational problem for a clamped loaded beam is studied with emphasis on the effect of the beam thickness, which appears as a parameter in the problem, on the accuracy. It is shown that the approximation achieved by a standard finite element method degenerates for thin beams. In contrast a large family of mixed finite element methods are shown to yield quasioptimal approximation independent of the thickness parameter. The most useful of these methods may be realized by replacing the integrals appearing in the stiffness matrix of the standard method by Gauss quadratures.
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    Numerische Mathematik 37 (1981), S. 387-404 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N20 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary The treatment of a multigrid method in the framework of numerical analysis elucidates that regularity of the solution is not necessary for the convergence of the multigrid algorithm but only for fast convergence. For the linear equations which arise from the discretization of the Poisson equation, a convergence factor 0,5 is established independent of the shape of the domain and of the regularity of the solution.
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    Numerische Mathematik 38 (1982), S. 141-154 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 35 A 40 ; 35 K 05 ; 65 N 15 ; 65 K 05 ; 80 A 20 ; CR: 5.17
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    Notes: Summary A nonlinear approximation technique for the numerical solution of certain free boundary problems is proposed. The method is shown for a degenerate one-dimensional Stefan problem. For this problem, an error estimate, which is independent of the used algorithm, is derived. Numerical examples are discussed.
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    Numerische Mathematik 40 (1982), S. 329-337 
    ISSN: 0945-3245
    Keywords: AMS (MOS): 65L05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary A widely used technique for improving the accuracy of solutions of initial value problems in ordinary differential equations is local extrapolation. It is well known, however, that when using methods appropriate for solving stiff systems of ODES, the stability of the method can be seriously degraded if local extrapolation is employed. This is due to the fact that performing local extrapolation on a low order method is equivalent to using a higher order formula and this high order formula may not be suitable for solving stiff systems. In the present paper a general approach is proposed whereby the correction term added on in the process of local extrapolation is in a sense a rational, rather than a polynomial, function. This approach allows high order formulae with bounded growth functions to be developed. As an example we derive anA-stable rational correction algorithm based on the trapezoidal rule. This new algorithm is found to be efficient when low accuracy is requested (say a relative accuracy of about 1%) and its performance is compared with that of the more familiar Richardson extrapolation method on a large set of stiff test problems.
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    Numerische Mathematik 40 (1982), S. 339-371 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; 65M20 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary In this first of two papers, computable a posteriori estimates of the space discretization error in the finite element method of lines solution of parabolic equations are analyzed for time-independent space meshes. The effectiveness of the error estimator is related to conditions on the solution regularity, mesh family type, and asymptotic range for the mesh size. For clarity the results are limited to a model problem in which piecewise linear elements in one space dimension are used. The results extend straight-forwardly to systems of equations and higher order elements in one space dimension, while the higher dimensional case requires additional considerations. The theory presented here provides the basis for the analysis and adaptive construction of time-dependent space meshes, which is the subject of the second paper. Computational results show that the approach is practically very effective and suggest that it can be used for solving more general problems.
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    Numerische Mathematik 41 (1983), S. 55-62 
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    Keywords: AMS(MOS): 65N30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary The finite element method with Laplace transform of time variable is proposed for the solution of hyperbolic equations. Error estimates in Hardy spaces of functions with values in Sobolev spaces are derived. Due to the isometric isomorphism of Hardy spaces with weighted Hilbert spaces these estimates are valid also for original formulations of hyperbolic equations.
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    Numerische Mathematik 41 (1983), S. 165-175 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65LO5 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary The extrapolated midpoint rule is a popular way to solve the initial value problem for a system of ordinary differential equations. As originally formulated by Gragg, the results are smoothed to remove the weak instability of the midpoint rule. It is shown that this smoothing is not necessary. A cheaper smoothing scheme is proposed. A way to exploit smoothing to increase the robustness of extrapolation codes is formulated.
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    Numerische Mathematik 41 (1983), S. 255-279 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L15 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Some methods for evaluating the characteristic exponents in connection with Newton's iteration are applied for solving the eigenvalue problem related to the finite Hill's differential equation or, in particular, Mathieu's equation. By using these methods a high accuracy is achieved, furthermore a complete error analysis, which yields rather realistic error bounds, is possible.
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    Numerische Mathematik 42 (1983), S. 15-30 
    ISSN: 0945-3245
    Keywords: AMS: 65L10 ; 34C25 ; 34K10 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary An iterative method is presented which starting from a lower or from an upper periodic solution, provides a monotone sequence converging to a periodic solution of (1). With some restrictions on the growth off, the method extends to functional differential equations of type (1′). Two numerical examples with an “a posteriori” error analysis are given.
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    Numerische Mathematik 42 (1983), S. 51-64 
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    Keywords: AMS (MOS): 65N99 ; 35L05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Engquist and Majda [3] proposed a pseudodifferential operator as asymptotically valid absorbing boundary condition for hyperbolic equations. (In the case of the wave equation this boundary condition is valid at all frequencies.) Here, least-squares approximation of the symbol of the pseudodifferential operator is proposed to obtain differential operators as boundary conditions. It is shown that for the wave equation this approach leads to Kreiss well-posed initial boundary value problems and that the expectation of the reflected energy is lower than in the case of Taylor- and Padé-approximations [3, 4]. Numerical examples indicate that this method works even more effectively for hyperbolic systems. The least-squares approach may be used to generate the boundary conditions automatically.
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    Numerische Mathematik 42 (1983), S. 77-95 
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    Keywords: AMS(MOS): 65N99 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Brakhage and Werner, Leis and Panich suggested to reduce the exterior Dirichlet boundary value problem for the Helmholtz equation to an integral equation of the second kind which is uniquely solvable for all frequencies by seeking the solution in the form of a combined double- and single-layer potential. We present an analysis of the appropriate choice of the parameter coupling the double- and single-layer potential in order to minimize the condition number of the integral operator.
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    Numerische Mathematik 42 (1983), S. 65-76 
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    Keywords: AMS(MOS): 65 N 20 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary We consider here a general class of algorithms for the numerical solution of variational inequalities. A convergence proof is given and in particular a multi-grid method is described. Numerical results are presented for the finite-difference discretization of an obstacle problem for minimal surfaces
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    Numerische Mathematik 42 (1983), S. 119-123 
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    Keywords: AMS(MOS): 65N10 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Many difference methods for the numerical solution of elliptic boundary value problems lead to systems of linear equations whose matrices areM-matrices and which therefore have nonnegative inverses. In this paper it is shown, that these difference methods are at most consistent of second order.
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    Numerische Mathematik 42 (1983), S. 173-194 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary We consider the stationary Navier-Stokes equations, written in terms of the primitive variables, in the case where both the partial differential equations and boundary conditions are inhomogeneous. Under certain conditions on the data, the existence and uniqueness of the solution of a weak formulation of the equations can be guaranteed. A conforming finite element method is presented and optimal estimates for the error of the approximate solution are proved. In addition, the convergence properties of iterative methods for the solution of the discrete nonlinear algebraic systems resulting from the finite element algorithm are given. Numerical examples, using an efficient choice of finite element spaces, are also provided.
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    Numerische Mathematik 42 (1983), S. 271-290 
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    Keywords: AMS(MOS): 65J10, 65L20, 65M10 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Consider a linear autonomous system of ordinary differential equations with the property that the norm |U(t)| of each solutionU(t) satisfies |U(t)|≦|U(0)| (t≧0). We call a numerical process for solving such a system contractive if a discrete version of this property holds for the numerical approximations. A givenk-step method is said to be unconditionally contractive if for each stepsizeh〉0 the numerical process is contractive. In this paper a general theory is given which yields necessary and sufficient conditions for unconditional contractivity. It turns out that unconditionally contractive methods are subject to an order barrierp≦1. Further the concept of a contractivity threshold is studied, which makes it possible to compare the contractivity behaviour of methods with an orderp〉1 as well. Most theoretical results in this paper are formulated for differential equations in arbitrary Banach spaces. Applications are given to numerical methods for solving ordinary as well as partial differential equations.
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    Numerische Mathematik 42 (1983), S. 359-377 
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    Keywords: AMS 65L05 ; 65L07 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary This paper is concerned with the stability of multistep methods for ordinary initial-value problems on grids with variable mesh-sizes. A necessary and sufficient condition for stability is given from which generalizations of recent results by Gear et al. and by Zlatev can be obtained as special cases. As an application the stability of the variable BDF-formulas is treated.
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    Numerische Mathematik 42 (1983), S. 379-389 
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    Keywords: AMS(MOS): 65L20 ; 15A60 ; 65M20 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary If the field of values of a matrixA is contained in the left complex halfplaneH and a functionf mapsH into the unit disc then ∥f(A)∥2≦1 by a theorem of J.v. Neumann. We prove a theorem of this type, only the field of values ofA is used for functions which are absolutely bounded by one in only part ofH. An extension can be used to show norm-stability of single step methods for stiff differential equations. The results are applicable among others to several subdiagonal Padé approximations which are notA-stable.
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    Numerische Mathematik 34 (1980), S. 171-187 
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    Topics: Mathematics
    Notes: Summary Difference methods for the numerical solution of linear partial differential equations may often be improved by using a weighted right hand side instead of the original right hand side of the differential equation. Difference formulas, for which that is possible, are called “Mehrstellenformeln’ or Hermitian formulas. In this paper the Hermitian formulas for the approximation of Laplace's operator are characterized by a very simple condition. We prove, that in two-dimensional case for a Hermitian formula of ordern at leastn+3 discretization points are necessary. We give examples of such optimal formulas of arbitrary high-order.
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    Numerische Mathematik 34 (1980), S. 457-467 
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    Keywords: AMS(MOS): 65L05, 65Q05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary By employing a numerical method which uses only rather classical tools of Numerical Analysis such as Newton's method and routines for ordinary differential equations, unstable periodic solutions of differential-difference equations can be computed. The method is applied to determine bifurcation diagrams with backward bifurcation.
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    Numerische Mathematik 35 (1980), S. 13-20 
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    Keywords: AMS (MOS): primary 65M05 ; 65M10 ; 65M15 ; secondary: 35M05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary We consider the numerical solution of the Tricomi problem. Using a weak formulation based on different spaces of test and trial functions, we construct a new Galerkin procedure for the Tricomi problem. Existence, uniqueness, and uniform stability of the approximate solution is proven, and a priori error bounds are given.
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    Numerische Mathematik 35 (1980), S. 21-33 
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    Keywords: AMS(MOS): 65B05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary The trapezoidal rule with deferred corrections using uncentered end formulas is shown to converge. While the proof technique is more specialized than the standard asymptotic expansion approach, it has some advantages. In addition to providing a more complete theoretical justification for current implementations of deferred corrections with the trapezoidal rule, the approach given here will hopefully apply for several other discretization methods.
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    Numerische Mathematik 35 (1980), S. 57-68 
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    Keywords: AMS(MOS): 65L05 ; 65M20 ; CR: 5.17
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    Notes: Summary This paper discussesrational Runge-Kutta methods for stiff differential equations of high dimensions. These methods are explicit and in addition do not require the computation or storage of the Jacobian. A stability analysis (based onn-dimensional linear equations) is given. A second orderA 0-stable method with embedded error control is constructed and numerical results of stiff problems originating from linear and nonlinear parabolic equations are presented.
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    Numerische Mathematik 44 (1984), S. 191-200 
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    Keywords: AMS (MOS): Primary 65M05, 65M10, 65M15 ; Secondary: 35M05 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary We consider the numerical solution of the boundary value problem (1) $$(1) Lu = k(y)u_{xx} + u_{yy} - c(x,y)u = f, u|_{\Gamma _0 \cup \Gamma _1 } = 0,$$ where $$k(y) \gtreqless 0$$ for $$y \gtreqless 0$$ Г 0 andГ 1 are parts of the boundary of a bounded simply connected regionG inR 2.G is bounded fory〉0 by a piecewise smooth curveГ 0 which intersects the liney=0 at the pointsA(−1,0) andB(0, 0). Fory〈0,G is bounded by a piecewise smooth curveГ 1 throughA, which meets the characteristic of (1) issued fromB at pointC, and by the curveГ 2 which consists of the portionCB of the characteristic throughB. Using a weak formulation based on different spaces of test and trial functions, we construct a Galerkin procedure for the above boundary value problem. Existence, uniqueness and uniform stability of an approximate solution is proven and a priori error bounds are given.
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    Notes: Summary The paper deals with such estimates of the rate of convergence of difference methods, which are compatible with the smoothness of the exact solutionu ∈ W 2 m (Ω),m〉0.5, of elliptic equations with mixed derivatives: The error in the norm of the discrete Sobolev spaceW 2 s (ω), ω denoting the set of grid points, is shown to be of the orderO(|h| m−s), 0≦s〈m.
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    Numerische Mathematik 44 (1984), S. 247-259 
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    Keywords: AMS (MOS): 65L05 ; 65M05 ; 65M20 ; CR: 5.17
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    Notes: Summary The aim of this paper is to study contractivity properties of two locally one-dimensional splitting methods for non-linear, multi-space dimensional parabolic partial differential equations. The term contractivity means that perturbations shall not propagate in the course of the time integration process. By relating the locally one-dimensional methods with contractive integration formulas for ordinary differential systems it can be shown that the splitting methods define contractive numerical solutions for a large class of non-linear parabolic problems without restrictions on the size of the time step.
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    Numerische Mathematik 36 (1980), S. 253-266 
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    Keywords: AMS(MOS): 65LO5 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary Single step exponentially fitted integration formulae of orders 4 and 6 are derived. The final approximation to the required solution is obtained via a linear combination of asymptotically less accurate solutions obtained using conventional implicit integration formulae. This linear combination is performed in such a way that the final integration formula, as well as having an increased order of accuracy, integrates a certain pre-determined ordinary differential equation exactly. The algorithms developed are illustrated by means of some numerical examples.
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    Numerische Mathematik 37 (1981), S. 105-120 
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    Topics: Mathematics
    Notes: Summary This study establishes an error estimate for a penalty-finite element approximation of the variational inequality obtained by a class of obstacle problems. By special identification of the penalty term, we first show that the penalty solution converges to the solution of a mixed formulation of the variational inequality. The rate of convergence of the penalization is ɛ where ɛ is the penalty parameter. To obtain the error of finite element approximation, we apply the results obtained by Brezzi, Hager and Raviart for the mixed finite element method to the variational inequality.
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    Numerische Mathematik 37 (1981), S. 333-337 
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    Notes: Summary A nonconforming mixed finite element method is presented for approximation of ∇w with Δw=f,w| r =0. Convergence of the order $$\left\| {\nabla w - u_h } \right\|_{0,\Omega } = \mathcal{O}(h^2 )$$ is proved, when linear finite elements are used. Only the standard regularity assumption on triangulations is needed.
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    Numerische Mathematik 38 (1982), S. 39-52 
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    Keywords: AMS (MOS): Primary 65L10 ; Secondary 35R35 ; CR: 5.17
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    Notes: Summary An approximate method for nonlinear problems with functional constraints is considered, in which the constraint in the whole domain is replaced by the constraint on a manifold of lower dimension. The stability criterion is introduced, and convergence theorems are proved for the onedimensional problem. Numerical results for the elastic-plastic torsion problem are given.
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    Numerische Mathematik 38 (1981), S. 255-261 
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    Keywords: AMS (MOS): 65N99 ; CR: 5.17
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    Notes: Summary This paper extends the earlier results by the author on two-dimensional free boundary problems. The main aim consists in derivation of an optimal error bound for the approximations of the free boundary.
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    Numerische Mathematik 38 (1981), S. 279-298 
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    Notes: Summary This paper deals with the solution of nonlinear stiff ordinary differential equations. The methods derived here are of Rosenbrock-type. This has the advantage that they areA-stable (or stiffly stable) and nevertheless do not require the solution of nonlinear systems of equations. We derive methods of orders 5 and 6 which require one evaluation of the Jacobian and oneLU decomposition per step. We have written programs for these methods which use Richardson extrapolation for the step size control and give numerical results.
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    Numerische Mathematik 38 (1982), S. 365-382 
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    Notes: Summary This paper considers the problems of minimizing Gateaux-differentiable functionals over subsets of real Banach spaces defined by a non-linear equality constraint. The existence of a Lagrange multiplier is proved, together with approximation results on the constrained subset, provided a nonlinear compatibility condition, generalizing the classical inf-sup condition, is satisfied. These ideas are applied to equilibrium problems in incompressible finite elasticity and lead to convergence results for these problems.
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    Numerische Mathematik 38 (1982), S. 447-453 
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    Notes: Summary As is known [4]. theC o Galerkin solution of a two-point boundary problem using piecewise polynomial functions, hasO(h 2k ) convergence at the knots, wherek is the degree of the finite element space. Also, it can be proved [5] that at specific interior points, the Gauss-Legendre points the gradient hasO(h k+1) convergence, instead ofO(h k ). In this note, it is proved that on any segment there arek−1 interior points where the Galerkin solution is ofO(h k+2), one order better than the global order of convergence. These points are the Lobatto points.
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    Numerische Mathematik 38 (1982), S. 467-471 
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    Topics: Mathematics
    Notes: Summary The approximation of linear systemsy′=−A(t)y+b(t) by backward differentiation methods up to order 5 is considered. It is proved that the error does not increase if the real symmetric matrixA(t) is positive definite andA′(t) is negative semi-definite.
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    Numerische Mathematik 39 (1982), S. 15-37 
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    Topics: Mathematics
    Notes: Summary We make several assumptions on a nonlinear evolution problem, ensuring the existence of a Hopf bifurcation. Under a fairly general approximation condition, we define a discrete problem which retains the bifurcation property and we prove an error estimate between the branches of exact and approximate periodic solutions.
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    Numerische Mathematik 39 (1982), S. 39-50 
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    Topics: Mathematics
    Notes: Summary In this paper we derive error estimates for infinite element method used in the approximation of solutions of interface problems. Furthermore, approximations of stress intensity factors are given. The infinite element method may be considered as a certain scheme of mesh refinement, but it has the advantages that the refinement is easy to be constructed that the stiffness matrix can be calculated efficiently, and that an approximate solution which has a singularity at the singular point can be also obtained.
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    Numerische Mathematik 34 (1980), S. 29-40 
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    Keywords: AMS(MOS): 65N25 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary A method is constructed which yields a strip containing the full solution sets of nonlinear eigenvalue problems of the formu=λTu. The strip can be narrowed iteratively, and the method applies for both stable and unstable branches. Its high degree of accuracy is demonstrated by numerical examples. In particular, a lower bound is given for the critical value at which criticality is lost in the thermal ignition problem for the unit ball.
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    Numerische Mathematik 34 (1980), S. 41-62 
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    Notes: Abstract This paper presents a new approach to the analysis of finite element methods based onC 0-finite elements for the approximate solution of 2nd order boundary value problems in which error estimates are derived directly in terms of two mesh dependent norms that are closely ralated to theL 2 norm and to the 2nd order Sobolev norm, respectively, and in which there is no assumption of quasi-uniformity on the mesh family. This is in contrast to the usual analysis in which error estimates are first derived in the 1st order Sobolev norm and subsequently are derived in theL 2 norm and in the 2nd order Sobolev norm — the 2nd order Sobolev norm estimates being obtained under the assumption that the functions in the underlying approximating subspaces lie in the 2nd order Sobolev space and that the mesh family is quasi-uniform.
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    Numerische Mathematik 34 (1980), S. 143-154 
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    Keywords: AMS(MOS): 65L65 ; CR: 5.17
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    Topics: Mathematics
    Notes: Summary In the first part [1] a general procedure is presented to obtain polynomial spline approximations for the solutions of initial value problems for ordinary differential equations; furthermore a divergence theorem is proved there. Sufficient conditions for convergence of the method are given in the second part [2]. The remaining case which has not been considered in [1] and [2] is treated in the present paper. In this special case the procedure is equivalent to an unstable two-step method with special initial values; nevertheless, convergence can be proved. Finally,A 0-stability of the method as well as the influence of rounding errors are investigated.
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    Numerische Mathematik 34 (1980), S. 1-13 
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    Keywords: AMS(MOS): 34A45, 34A50, 65L05 ; CR: 5.17
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    Notes: Summary In this paper Lie series are presented in Chebyshev form and applied to the iterative solution of initial value problems in differential equations. The resulting method, though algebraically complicated, is of theoretical interest as a generalisation of Taylor series methods and iterative Chebyshev methods. The theory of the method is discussed and the solutions of some simple scalar equations are analysed to illustrate the behaviour of the process.
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    Notes: Summary The ALGOL-procedure1 char2 presented in this paper can be applied to the initial or initial-boundary value problem of a quasilinear hyperbolic differential equation of second order. A method of characteristics is combined with extrapolation to the limit. Thus, the results are very accurate. The same accuracy can also be obtained if the initial values are only piecewise smooth.
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    Numerische Mathematik 43 (1984), S. 419-437 
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    Notes: Summary In this paper, we consider monotone explicit iterations of the finite element schemes for the nonlinear equations associated with the boundary value problem Δu=bu 2, based on piecewise linear polynomials and the lumping operator. These iterations construct the monotonically decreasing and increasing sequences, and convergence proofs are given. Finally, we present some numerical examples verifying the effectiveness of the theory.
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    Numerische Mathematik 43 (1984), S. 463-483 
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    Notes: Summary The method of lines is used to semi-discretize the non-linear Poisson equation over a domain with a free boundary. The resulting multipoint free boundary problem is solved with a line Gauss-Seidel method which is shown to converge monotonically. The method of lines solution is then shown to converge to the continuous solution of the variational inequality form of the obstacle problem. Some numerical results for the diffusion-reaction equation indicate that the method is applicable to more general free boundary problems for nonlinear elliptic equations.
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    Numerische Mathematik 36 (1980), S. 1-25 
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    Notes: Summary We begin in this paper the study of a general method of approximation of solutions of nonlinear equations in a Banach space. We prove here an abstract result concerning the approximation of branches of nonsingular solutions. The general theory is then applied to the study of the convergence of two mixed finite element methods for the Navier-Stokes and the von Kármán equations.
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    Numerische Mathematik 36 (1980), S. 33-52 
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    Notes: Summary A modified variational formulation, recently introduced by Taylor, Beresford and Wilson for solving second order problems, using the nonconforming Wilson element is here analysed. It is shown that the Patch Test is satisfied and that stresses and displacements are respectively first and second order accurate for arbitrary quadrilateral meshes.
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    Numerische Mathematik 36 (1980), S. 73-98 
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    Keywords: AMS: 35R35, 65P05, 76S05 ; CR: 5.17
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    Notes: Summary A new numerical method is used to solve stationary free boundary problems for fluid flow through porous media. The method also applies to inhomogeneous media, and to cases with a partial unsaturated flow.
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    Notes: Summary In this paper we describe a nonconforming finite element method to compute the MHD spectrum of a plasma in a toroïdal configuration. We show that this method leads to a good approximation of the spectrum.
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    Numerische Mathematik 37 (1981), S. 1-28 
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    Notes: Summary We continue here the study of a general method of approximation of nonlinear equations in a Banach space yet considered in [2]. In this paper, we give fairly general approximation results for the solutions in a neighborhood of a simple limit point. We the apply the previous analysis to the study of Galerkin approximations for a class of variationally posed nonlinear problems and to a mixed finite element method for the NavierStokes equations.
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    Numerische Mathematik 37 (1981), S. 61-91 
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    Notes: Summary Stability regions of explicit “linear” time discretization methods for solving initial value problems are treated. If an integration method needsm function evaluations per time step, then we scale the stability region by dividing bym. We show that the scaled stability region of a method, satisfying some reasonable conditions, cannot be properly contained in the scaled stability region of another method. Bounds for the size of the stability regions for three different purposes are then given: for “general” nonlinear ordinary differential systems, for systems obtained from parabolic problems and for systems obtained from hyperbolic problems. We also show how these bounds can be approached by high order methods.
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    Numerische Mathematik 43 (1984), S. 309-327 
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    Notes: Summary Diffusion problems occuring in practice often involve irregularities in the initial or boundary data resulting in a local break-down of the solution's regularity. This may drastically reduce the accuracy of discretization schemes over the whole interval of integration, unless certain precautions are taken. The diagonal Padé schemes of order 2μ, combined with a standard finite element discretization, usually require an unnatural step size restriction in order to achieve even locally optimal accuracy. It is shown here that this restriction can be avoided by means of a sample damping procedure which preserves the order of the discretization and, in the case μ=1, does not increase the costs.
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    Numerische Mathematik 43 (1984), S. 343-360 
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    Notes: Summary Retarded initial value problems are routinely replaced by an initial value problem of ordinary differential equations along with an appropriate interpolation scheme. Hence one can control the global error of the modified problem but not directly the actual global error of the original problem. In this paper we give an estimate for the actual global error in terms of controllable quantities. Further we show that the notion of local error as inherited from the theory of ordinary differential equations must be generalized for retarded problems. Along with the new definition we are led to developing a reliable basis for a step selection scheme.
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    Numerische Mathematik 43 (1984), S. 389-396 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Stability analysis of θ-methods for functional differential equations based on the test equation $$\begin{gathered} y'(t) = ay(t - \lambda ) + by(t),t 〉 0 \hfill \\ y(t) = \psi (t),t \in \left[ { - \lambda ,0} \right] \hfill \\ \end{gathered} $$ λ〉0, is presented. It is known thaty(t)→0 ast→∞ if and only if |b|〈−a and we investigate whether this property is inherited by the numerical solution approximatingy.
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  • 99
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 44 (1984), S. 75-102 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper examines the concepts of feedback and adaptivity for the Finite Element Method. The model problem concernsC 0 elements of arbitrary, fixed degree for a one-dimensional two-point boundary value problem. Three different feedback methods are introduced and a detailed analysis of their adaptivity is given.
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  • 100
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 44 (1984), S. 201-217 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N30 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Description / Table of Contents: Resumé On présente une méthode d'approximation numérique des équations de Navier-Stokes possédant une direction de périodicité. Dans cette direction une méthode pseudospectrale basée sur des développements en série de Fourier est utilisée, dans les deux autres on applique une méthode d'éléments finis standard. On montre que la convergence est optimale et que les deux paramètres de discrétisation peuvent être choisis de façon indépendante.
    Notes: Summary We present a method for the numerical approximation of Navier-Stokes equations with one direction of periodicity. In this direction a Fourier pseudospectral method is used, in the two others a standard F.E.M. is applied. We prove optimal rate of convergence where the two parameters of discretization intervene independently.
    Type of Medium: Electronic Resource
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